A research study to determine if the recurrence of Hepatitis B (HBV) virus after liver transplantation (OLT) can be delayed or prevented by the administration of hepatitis B immune globulin (H-BIG). The subjects of this study are patients who have end stage liver disease due to Hepatitis B and who have been accepted as candidates for liver transplantation. The HBV virus recurs in virtually all such patients, although the pace of hepatitis appears accelerated and progression to liver failure and/or cirrhosis occurs within one or two years following OLT. The primary objective of this study is to provide investigational H-BIG to prevent HBV reinfection following OLT in patients with end stage liver disease due to HBV. The secondary objectives of this study are to expand the safety profile of the H-BIG administered to OLT patients and to collect data on anti-HBs levels in patients receiving H-BIG as these data are relevant to understanding any recurrence of HBV infection after transplantation. Initially, H-BIG, 20,000 IU, will be administered intravenously at the time of the transplant operation. Then H-BIG will be given intramuscularly, daily for one week until adequate blood levels of antibodies to HBV have been achieved. Further dosing will be based on serum levels of anti-HBV antibodies. Qualifying subjects, for the first three months following transplantation must be monitored for the presence of HBV infection according to the standard of practice at the clinical sight. During this 90 days, anti-HB levels must be obtained whenever HBsAg levels are obtained. The tests will be evaluated by the investigator. Follow up will consist of periodic blood testing for HBV. If found positive for HBsAg and/or HBV DNA, lamivudine will be given as standard care.